1598 constant and variable capital

constant and variable capital Macmillan. Palgrave 1 Definition In Das Kapital Marx defined Constant Capital as that part of capital advanced in the means of Licensee: production; he defined Variable Capital as the part of capital advanced in wages (Marx, 1867,

Vol. I, ch. 6). These definitions come from his concept of Value: he defined the value of permission. commodities as the amount of labour directly and indirectly necessary to produce commodities without (Vol. I, ch. 1). In other words, the value of commodities is the sum of C and N, where C is the value of the means of production necessary to produce them and N is the amount of labour used distribute that is directly necessary to produce them. The value of the capital advanced in the means of or production is equal to C. copy However, the value of the capital advanced in wages is obviously not equal to N, because it not may

is the value of the commodities which labourers can buy with their wages, and has no direct You relationship with the amount of labour which they actually expend. Therefore, while the value of the part of capital that is advanced in the means of production is transferred to the value of the products without quantitative change, the value of the capital advanced in wages undergoes quantitative change in the process of transfer to the value of the products. This is the reason why Marx proposed the definitions of constant capital C and variable capital V. The definition of constant capital and variable capital must not be confused with the definition of fixed capital and liquid capital. Fixed capital is a part of constant capital which is www.dictionaryofeconomics.com. totally used in production process but transfers its value to products only partially. Liquid capital

is a part of constant capital which is totally used up and transfers its whole value within one Economics. production process. So constant capital is composed of both fixed capital and liquid capital, and of on the other hand liquid capital belongs partly to constant capital and partly to variable capital. Marx introduced the concept ‘value-composition of capital’, μ, which is defined as the ratio Dictionary

of constant capital C to variable capital V: Palgrave

C New

μ ≡ . (1.1) The V Marx knew well that the value composition of capital reflects not only material characteristics of the process of production but also the social relationship between capitalists and labourers. In Macmillan. fact definition (1.1) can be rewritten as ©Palgrave CN μ = ⋅ (1.2) NV 1599 constant and variable capital

C/N reflects the character of the process of production and N/V reflects the class relationship between capitalists and labourers. C/N is the ratio of the amount of labour necessary to produce the means of production to the amount of labour directly bestowed, which is completely Macmillan. determined by the material condition in the process of production, while N/V is the ratio of the amount of labour which labourers actually expend to the amount of labour that is necessary in Palgrave order to produce commodities which labourers can purchase with their wages. If labourers are forced to work longer with less wages, this ratio must rise. Licensee: Marx proposed to call the value-composition of capital, insofar as it is determined by the

material condition of the process of production, ‘the organic composition of capital’. More permission. explicitly, ‘The value-composition of capital, inasmuch as it is determined by, and reflects, its technical composition, is called the organic composition of capital’ (Capital, Vol. III, ch. 8). without However, as shown above, the value composition of capital is not determined by the material distribute condition of the process of production alone. So it is better to introduce the ratio C/N in the place or

of the organic composition of capital, which is determined only by the material condition in the copy process of production. In order to avoid confusion, I call this ratio the ‘organic composition of not production’. This is the ratio of dead labour to living labour, which Marx himself frequently used may in Das Kapital. You

2 Variable Capital and Source of Profit In contrast to Smith, Ricardo and others, Marx attached great importance to analysis to find the source of profit. He found that source in surplus labour, which is the excess of labour expended by labourers over the value of commodities which labourers can obtain with their wages

(Capital, vol. I, ch. 5). Using the notation introduced above, N > V is the necessary condition for www.dictionaryofeconomics.com. profit to exist. In order to illuminate this fact, he called capital advanced in wages Variable

Capital. So the validity of this name depends on his analysis of the source of profit. How is it Economics. justified? of For simplicity we set up the simplest model which can reflect the fundamental characteristics of a capitalistic economy; these characteristics are the prevalence of commodity Dictionary production, and the existence of class relationships between labourers and capitalists. There are Palgrave only two kinds of commodities: the means of production (commodity 1) and consumption goods New

(commodity 2). In order to produce one unit of the ith commodity an amount of ai unit of means The of production and an amount of labour τ i are necessary as input. Labourers are forced to work for T hours per day and earn the money wage rate w. Macmillan. In order for profit to exist in both industries the following inequalities are necessary

p1111>+apτ w (2.1) ©Palgrave

p2212>+apτ w (2.2) 1600 constant and variable capital

where p1 and p2 denote the price of the means of production and consumption goods respectively. As labourers work for T hours a day at money wage w per hour, they can purchase an amount B of consumption goods. Macmillan. wT BBTR= , = (2.3) Palgrave p2

where R is the real wage rate. Licensee: In the first volume of Das Kapital, Marx assumed that all commodities are exchanged at prices exactly proportionate to their unit value (equivalent exchange). Unit values of permission. commodities are determined by the following equations without tat1111= +τ (2.4)

tat2212= +τ (2.5) distribute or

which assure unique and positive values, provided a1 <1 (Dmitriev, 1898; May, 1949–50; copy

Okishio, 1955a, 1955b). not Under the assumption of equivalent exchange, we have may You

pii= λt (2.6) where λ is a constant which converts the dimension from hours to, say, dollars. Substituting (2.3) and (2.6) into (2.1) and (2.2) we get B tat>+τ t (2.7) 11112T

B www.dictionaryofeconomics.com. tat>+τ t (2.8) 22122T

By equations (2.4) and (2.5) and the above inequalities, we have Economics. of ⎛⎞B τ12⎜⎟10− t > (2.9) ⎝⎠T Dictionary B ⎛⎞ Palgrave τ 22⎜⎟10− t > (2.10)

⎝⎠T New Consequently we arrive at the conclusion The

TBt> 2. (2.11) Macmillan. This inequality implies the existence of surplus value, because surplus value is the excess of working hours T over the amount of labour necessary to produce commodities which labourers ©Palgrave can receive with wages B. If the number of workers employed is n, then total expended labour is 1601 constant and variable capital

nT and variable capital measured in terms of value is Bt2n. So the inequality (2.11) can be rewritten as

NV> (2.12) Macmillan. This is the reason Marx called capital advanced in wages variable capital. Palgrave As shown above, Marx proved the theorem of the source of profit under the assumption of

equivalent exchange. Though this is a clear-cut way to show the results, it has induced various Licensee: critiques. Many critics have said that Marx’s theorem would be right if all exchanges were equivalent exchange, but that in reality exchanges are seldom equivalent so his theorem cannot be valid. In order to refute such a criticism we must prove the theorem without the assumption of permission.

equivalent exchange (see Okishio 1955a, 1955b, 1963, 1972, 1978; Morishima, 1973). without Mathematically, our task is to find necessary and sufficient conditions for inequalities (2.1), (2.2) and (2.3) to have non-negative solutions for p1, p2. From (2.1) we know easily that the condition distribute or

10− a1 > (2.13) copy not is necessary for p1 to be positive. This condition ensures that the society will obtain net output. may

Next, substituting (2.3) into (2.1), and from (2.13) we have You pBτ 11> . (2.14) p21Ta()1− On the other hand, from (2.2) and (2.3) we get p TB−τ 12> . (2.15) pTa22 www.dictionaryofeconomics.com. We can easily get from (2.14) and (2.15)

aB21τ Economics.

<−TBτ 2 . (2.16) of ()1− a1

Inequality (2.16) is rewritten as Dictionary ⎛⎞a τ

21 Palgrave TB>+⎜⎟τ 2 . (2.17)

⎝⎠1− a1 New The By (2.17), (2.4) and (2.5) the above becomes TBt> . (2.18)

2 Macmillan. Thus we can arrive at Marx’s result.

For later convenience we show another expression for the existence of surplus value. ©Palgrave Dividing (2.1) and (2.2) by w, we get 1602 constant and variable capital

pp 11>+a τ (2.19) ww11

pp Macmillan. 21>+a τ (2.20) ww22 Palgrave By comparing (2.19) and (2.20), and (2.4) and (2.5), we get

p Licensee: i >=ti,(1,2) (2.21) w i

Equation (2.21) implies that if positive profit exists, then the price–wage ratio (the amount of permission. commanded labour) is greater than the amount of value (necessary labour). In the famous controversy with Ricardo, Malthus pointed out this difference between labour commanded and without labour embodied. Though he wrongly thought that this difference injured the validity of the distribute labour theory of value, he had come near to the Marxian theory of the source of profit (see or

Malthus, 1820, pp. 61–3, 120). copy Condition (2.21) is rewritten as not may You 1 twpii>

This condition shows that if positive profit exists, then the productivity of labour ()1 ti must be greater than the rate of real wages ()wpi .

3 Organic Composition and Production Price

www.dictionaryofeconomics.com. The concept of organic composition of capital plays an important role in Marx’s analysis of prices. Economics.

The price of production (Ricardo’s ‘natural price’) that gives every industry the equal rate of of profit is determined by the following equations: Dictionary p1111=+(1 rap)( +τ w) (3.1) Palgrave p2212=+(1 rap)( +τ w) (3.2) New

wRp= 2 (3.3) The where r is the general (equal) rate of profit. The first problem is to examine the relationship between Macmillan.

tp ©Palgrave 11~. tp22 1603 constant and variable capital

If they are equal then we have equivalent exchange, if not we have non-equivalent exchange from the point of view of the labour theory of value. The values of the commodities are determined by (2.4) and (2.5). The ratio of the value of production-goods to consumption-goods Macmillan. tt12 is given as Palgrave ⎛⎞at11 τ1 ⎜⎟+1 t1 τ1

⎝⎠ Licensee: = . (3.4) t2 ⎛⎞at21 τ 2 ⎜⎟+1 ⎝⎠τ 2 permission. The relative price of production-goods to consumption-goods determined by (3.1) and (3.2) is given as without

⎛⎞ap11 distribute τ1 ⎜⎟+ w or p1 ⎝⎠τ1 = . (3.5) copy

p2 ⎛⎞ap21 not τ 2 ⎜⎟+ w may ⎝⎠τ 2 You Comparing (3.4) with (3.5), we obtain ⎡ at a p ⎤ 11++1 1 1 w tpττ⎢ τ ⎥ 1111−=⎢ − 1 ⎥. (3.6) tpτ at a p 222⎢ 21++1 2 1 w⎥ ⎢ ⎥ ⎣ ττ22⎦

The expression in brackets on the RHS of (3.6) is given by www.dictionaryofeconomics.com. ⎛⎞aa = tw−− p12 A,0. A > (3.7) [] ()11⎜⎟ Economics.

⎝⎠ττ12 of

If profit is positive, from (2.21) tw11− p is negative. So we can conclude Dictionary tp aa 11QP⇔ 12. (3.8)

tp22τ 12τ Palgrave The RHS of the above means the comparison of the organic composition of production and also New The the organic composition of capital, because as shown above the organic composition of production is atii1 τ and the organic composition of capital is atii12τ Rt . The second problem is to examine the influence of the change in real wage rate on the Macmillan. relative prices determined by (3.1), (3.2) and (3.3): ©Palgrave

⎛⎞p dd.⎜⎟1 R ⎝⎠p2 1604 constant and variable capital

Denoting the relative price of production-goods to consumption-goods as p, from (3.1), (3.2) and (3.3) we obtain

2 Macmillan. fp( ) ≡ ap2211+−−=(ττ Rap) R 0. (3.9)

Differentiating (3.9) with respect to R, we have Palgrave

dp τ12−τ p

= . (3.10) Licensee: d2R ap221+τ R− a The denominator above is positive, because from (3.9) permission.

2 denominator × pap=+>21τ R0. without

We shall show that the sign of the numerator depends on the comparison between the organic distribute or composition of capital in both sectors. copy

The function f(p) in (3.9) is drawn in Figure 1. The meaningful solution of the equation not

(3.9) is given at p*. Substituting τ12τ into f(p), we get may You

⎛⎞τ1 faa⎜⎟=−τ12122()ττ. ⎝⎠τ 2

Therefore if aa21τ −> 12τ 0 then f ()ττ12> 0 , so considering the graph of f(p) we know that * ττ12> p . In the same way we can conclude that if aa21ττ− 12Q 0 , then ττ12/ Q p .

Consequently, from (3.10) we can conclude www.dictionaryofeconomics.com.

⎛⎞pa11a2 dR⎜⎟d0QP⇔ . Economics. ⎝⎠p21τ τ 2 of

This proposition is first established in Ricardo’s Principles (1821, p. 43). Dictionary

4 Organic Composition and the Rate of Profit Palgrave New

The concept of organic composition of capital plays an important role in Marx’s analysis of the The movement of the rate of profit.

Macmillan.

©Palgrave

1605 constant and variable capital Macmillan. Palgrave Licensee: permission. without distribute or copy not may You

Figure 1 Marx defined the rate of profit as S r = . (4.1) CV+ www.dictionaryofeconomics.com. By (1.1), equation (4.1) is rewritten as

e Economics.

reSV==, (4.2) of μ +1

where e is the rate of exploitation. Dictionary He asserted that if the organic composition of capital μ increases sufficiently then the rate of profit r must inevitably decrease. This is the famous ‘law of the tendency for the rate of profit Palgrave to fall’ (Capital, vol. III, ch. 13). New Many people have criticized this theorem. They have said that if the rate of exploitation e The increases sufficiently, r may increase in spite of the increase of μ. So r does not necessarily decrease, even if μ increases sufficiently (Robinson, 1942; Sweezy, 1942). Such a critique Macmillan. overlooks the logic of Marx’s argument.

Marx stated: ©Palgrave Since the mass of the employed living labour is continually on the decline as compared to the mass of materialized labour set in motion by it, i.e., to the productively consumed 1606 constant and variable capital

means of production, it follows that the portion of living labour, unpaid and congealed in surplus-value, must also be continually on the decrease compared to the amount of value represented by the invested total capital. Since the ratio of the mass of surplus-value to Macmillan. the value of the invested total capital forms the rate of profit, this rate must constantly fall

(Capital, vol. III, ch. 13, p. 213). Palgrave Therefore Marx’s true intention is to insist that if the organic composition of production v

= C/N (the ratio of the mass of materialized labour to the mass of living labour) increases Licensee: sufficiently, the rate of profit must fall.

This can be proved as follows (Okishio, 1972). From (4.1) and (4.2), and permission. vCN= (4.3) without we have distribute

St+1 or rrtt+1 −= − r t CVtt++11+ copy not et+1 =−r (4.4) may ve11++t tt++11() You 1 =−rt vett++11()111++ e t + 1 where suffixes t, t + 1 denote periods. The RHS of (4.4) is an increasing function of e. If we take the limiting value as e tends to infinity, we have www.dictionaryofeconomics.com. 1 rrtt+1 − <− r t. vt+1 Economics. of

Therefore we conclude, if vrtt+1 >1 , then rrtt+1 − < 0 .

The above reasoning can be restated. The reciprocal of the organic composition of Dictionary production sets an upper limit to the rate of profit, because Palgrave SSVN+ r = <= (4.5) New

CV+ C C The If this upper limit decreases sufficiently, the rate of profit must eventually decrease, as shown in

Figure 2. Macmillan.

©Palgrave 1607 constant and variable capital

Macmillan.

Palgrave

Licensee:

permission.

without

distribute

or

copy

not may You

www.dictionaryofeconomics.com.

Economics.

Figure 2 of

In response to criticisms of this view we must say that as far as we accept Marx’s assumption Dictionary that the inverse of the organic composition (N/C) tends toward zero, Marx’s conclusion inevitably follows. Palgrave New

So far we have defined the rate of profit as (4.1) and C, V, S are all measured in terms of The labour value. However, the general rate of profit r must be determined by (3.1), (3.2) and (3.3). Can we derive the same conclusions for such a redefined r? Macmillan. Eliminating p1, p2, w from (3.1), (3.2) and (3.3) we have

2 frR()()(,1≡+ r Raττ − a ) ©Palgrave 12 21 (4.6) − ()()110+++=ra12τ R Differentiating f(r, R) we have 1608 constant and variable capital

frrRdd0+= fR (4.7) where Macmillan. fr =+21()rRa( 12ττ − a 21) −+( a 1 τ 2 R) 2 Palgrave fraarR =+()(1112ττ − 21 )() −+ τ 2

Considering (4.6) Licensee:

()112+=++−rfr ( a12τ R)( r) (4.8)

From (3.1), (3.2), (3.3), we know permission. without 11−+( ra) 12 > 0 11 −+( r)τ R > 0 (4.9)

From (4.8) frR< 0. f is rewritten as distribute or

fR =+()()11 r{⎣⎦⎡⎤ + ra12 − 11τ −+ () ra 21τ } copy not

So by (4.9) fR < 0, from which ddrR< 0. As R goes to zero r tends to its upper limit, which is may obtained from (4.6) You

1− a1 rmax = . (4.10) a1 Since the value of the means of production is determined by (2.4), we have 1− aN(1− at) τ 111===11 (4.11)

aatatC111111 www.dictionaryofeconomics.com. Thus the upper limit of the general rate of profit is given by the reciprocal of the organic

composition of production in the means of production sector. Therefore if the organic Economics. composition in that sector rises sufficiently, the general rate of profit must fall. of

5 Organic Composition and Unemployment Dictionary

The concept of organic composition of capital plays an important role in Marx’s analysis of the Palgrave

movement of employment (Capital, vol. I, ch. 23). New

Marx assumed a rise in labour productivity to accompany the rise in the organic The composition of production C/N. If C/N rises then from the definition of organic composition the

amount of employment must decrease relative to constant capital. Macmillan. However, how does the increase in the organic composition influence the absolute level of

employment? ©Palgrave Many people thought that even if C/N rises sufficiently, still if constant capital C also increases then the absolute level of employment can also increase, though less than 1609 constant and variable capital

proportionately to constant capital (Oppenheimer, 1903). But by reasoning similar to that used for ‘the tendency of the rate of profit to fall’, we can prove that if organic composition rises sufficiently, then the absolute level of employment must actually decrease. Macmillan.

The organic composition of production in the tth period vt is defined as Palgrave Ct vt = . (5.1) Nt Licensee:

The accumulation of constant capital ΔCC=−tt+1 C is financed from surplus value S.

CCSttt+1 − < . (5.2) permission.

The surplus value S is a part of the amount of living labour which labourers expend without

SNtt< . (5.3) distribute

By (5.1), we obtain, or copy

11 not

NN−= C − C may tt++11vv t t

tt+1 You

111⎛⎞ =−+−()CCCttt+1 ⎜⎟. vvvttt++11⎝⎠

From (5.2) and (5.3) we get

11111⎛⎞N ⎛⎞

t www.dictionaryofeconomics.com. NNtt+1 −< SC tt +⎜⎟ − < + C t ⎜⎟ − vvvvvvtttttt++++1111⎝⎠ ⎝⎠

Ct =+−()1.vvtt+1 Economics. of vvtt+1 Dictionary we can say, if ()10+−vvtt+1 < then NNtt+1 − < 0 . Therefore, if the organic composition of production in the t + 1th period, vt+1, increases sufficiently so as to exceed 1+vt, then the amount Palgrave of employed labourer, Nt+1 must inevitably become less than Nt, however high the rate of New

accumulation of capital may be (Okishio, 1972). The rate of accumulation of capital ΔCC itself The is bounded by the reciprocal of the organic composition. From (5.2) and (5.3)

ΔCN1 Macmillan. < = CCv ©Palgrave 1610 constant and variable capital

so that, because it is reasonable to assume that the growth rate of labour supply is non-negative, we can say that if the organic composition rises sufficiently the rate of unemployment inevitably rises. Though Marx did not state this explicitly, we think that this is what he wanted to say. Macmillan. In analysing Marx’s theorem on the movement of the rate of profit and employment, we have accepted his central assumption that the organic composition of production rises Palgrave sufficiently over time. However, there arises the problem: under what conditions do capitalists choose techniques that have sufficiently high organic compositions of production? Licensee: Marx seemed to think that the rise in labour productivity and the rise in the organic

composition are two aspects of the same thing. But these two do not always go together. Marx permission. himself knew that if labour productivity in the means of production sector rises very high then even if technical composition rises, still the value composition may remain constant or decrease. without As to the capitalists’ introduction of new techniques we have the following propositions: distribute

(1) if the real wage rate remains constant and capitalists introduce new techniques which or

raise the rate remains of profit (calculated at the current prevailing prices and wage) then the new copy general rate of profit does not decrease, whatever the organic composition may be. not (2) if the real wage rate rises and capitalists adapt to this situation with the introduction of may new techniques, then the new general rate of profit does is higher than the one which would be You expected if such a new technique were not introduced. For the proofs of these propositions, see CHOICE OF TECHNIQUE AND THE RATE OF PROFIT.

N. Okishio

www.dictionaryofeconomics.com. See also Economics.

Marxian value analysis; organic composition of capital; surplus value. of

Bibliography Dictionary Dmitriev, V.K. 1898. The theory of value of David Ricardo. In V.K. Dmitriev, Economic Essays

on Value, Competition and Utility, ed. D.M. Nuti, Cambridge: Cambridge University Press, Palgrave

1974. New

Malthus, R. 1820. Principles of Political Economy considered with a View to their Practical The Application. 1st edn, London.

Marx, K. 1867–94. Capital. Translated from the third German edition by Samuel Moore and Macmillan. Edward Aveling, ed. Frederick Engels. New York: International Publishers, 1967. May, K. 1949. The structure of classical theories. Review of Economic Studies 17(1), 60–69. ©Palgrave Morishima, M. 1973. Marx’s Economics: A Dual Theory of Value and Growth. Cambridge: Cambridge University Press. 1611 constant and variable capital

Okishio, N. 1955a. Kachi to Kakaku (Value and production price). Keizaigaku Kenkyu Nempo (The Annals of Economic Studies), Kobe University, No. 19. Okishio, N. 1955b. Monopoly and the rates of profit. Kobe University Economic Review 1, 71– 88. Macmillan. Okishio, N. 1963. A mathematical note on Marxian theorems. Weltwirtschaftliches Archiv 91, pt. 2, 287–98. Palgrave Okishio, N. 1972. A formal proof of Marx’s two theorems. Kobe University Economic Review 18, 1–6. Licensee: Okishio, N, et al. 1978. Three topics on Marxian fundamental theorems. Kobe University

Economic Review 24, 1–18. permission. Oppenheimer, T. 1903. Das Grundgesetz der Marxschen Gesellschaftslehre. Book II, ch. 25. Berlin: Reimer. without Ricardo, D. 1821. On the Principles of Political Economy and Taxation. Vol. 1 in Works and distribute

Correspondence of David Ricardo, ed. P. Sraffa, Cambridge: Cambridge University Press, or 1951–73. copy

Robinson, J. 1942. An Essay on Marxian Economics. London: Macmillan. not

Sweezy, P.M. 1942. The Theory of Capitalist Development: Principles of Marxian Political may

Economy. New York: Oxford University Press. You

www.dictionaryofeconomics.com. Economics. of Dictionary Palgrave New The Macmillan. ©Palgrave